Simplify the following expression: $ r = \dfrac{9z + 5}{-2z - 4} + \dfrac{-3}{10} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{10}{10}$ $ \dfrac{9z + 5}{-2z - 4} \times \dfrac{10}{10} = \dfrac{90z + 50}{-20z - 40} $ Multiply the second expression by $\dfrac{-2z - 4}{-2z - 4}$ $ \dfrac{-3}{10} \times \dfrac{-2z - 4}{-2z - 4} = \dfrac{6z + 12}{-20z - 40} $ Therefore $ r = \dfrac{90z + 50}{-20z - 40} + \dfrac{6z + 12}{-20z - 40} $ Now the expressions have the same denominator we can simply add the numerators: $r = \dfrac{90z + 50 + 6z + 12}{-20z - 40} $ $r = \dfrac{96z + 62}{-20z - 40}$ Simplify the expression by dividing the numerator and denominator by -2: $r = \dfrac{-48z - 31}{10z + 20}$